Unit One Test
What does "k" determine?
-If 0<|k|<1 (decimal): horizontal stretch by a factor of 1/|k| -If |k|>1: horizontal compression by a factor of 1/|k| -if k<0: reflection in the y-axis
What does "a" determine
-if |a|>1: vertical stretch by a factor of |a| -if 0<|a|<1 (a is a decimal): vertical compression by a factor of |a| - if a<0 (negative): reflection in the x-axis
Rules for listing domain and range
-smalles to largest -do not repeat if they appear more than once
How can relations be represented?
1. equation 2. graph 3. table of values 4. ordered pairs 5. mapping diagram
a) g(3)=2 b) g(-1)=0 c) g(0)=1
Determine each value a) g(3) b) g(-1) c) g(0)
a)relation b)function
Determine whether or not the following graphs represent functions
line w/ one arrow
Domain:{x∈R|x≤3} Range:{y∈R|y≥-1}
Parabola
Domain:{x∈R} Range:{y∈R|y≤3}
Line w/two arrows
Domain:{x∈R} Range:{y∈R}
How to obtain the inverse from an equation
Interchange x and y and solve for y
The real number set
Real number set→R: -natural numbers (1,2,3...)→N -whole numbers (0,1,2,3...)→W -integers (...-3,-2,-1,0,2,3...)→I -rational numbers (a/b, b≠0)→Q
*don't forget squiggly thing at beginning and end of list* a) domain: {-2,-1,0,3} range: {-1,0,2,4,5} b) domain: {-3,-2,0,1,2} range: {-8,-4,0,6}
State the domain and range of each of the following
Switch
State the domain and range of each of the following
How to obtain the inverse from a set of points/graph
Swap the coordinates of the points
:)
Switch back
What does the graph of the inverse function look like?
The graph is the reflection of f(x) in the line y=x
What happens if there is no a or k value
They equal 1
1. Function 2. Relation 3. Function
Which of the following represents a function?
a) Function b) Relation (because 2 y-values for 15)
Which of the following represents a function?
a) function b) Relation c) Relation
Which of the following represents a function?
asymptote
a line that the function approaches but never crosses or touches
Function
a relation in which every x-coordinate corresponds to only one y-coordinate
A relation is a function if... (equation)
an x-value only gives one y-value when subbed into an equation (the exponeny of y must be odd)
Use function notation to evaluate for x=2 when y=3x-4
f(x)=3x-4 f(2)=3(2)-4 f(2)=2
How to explain in words why/why not something is a function
function: because every x-value has only one corresponding y-value relation: because not every x-value has only one corresponding y-value
a) function b)relation
identify which represent a function
a)function b)relation c)function
identify which represent a function
Relation
relationship between two variables
absolute value
the distance from x to 0 (written as |x|) →EX: |-2|=2
Range
the set of all values of the dependent variable in a relation (all the y-values)
Domain
the set of all values of the independent variable in a relation (all the x-values)
A relation is a function if... (mapping diagram)
there is only 1 arrow leaving each of the x-coordinates in a mapping diagram
A relation is a function if... (graph)
vertical line test→a vertical line intersects only one point on a graph
A relation is a function if... (ordered pairs and table of values)
x-coordinate doesn't repeat in a set of ordered pairs or table of values
function notation
y=3x-4 changes to f(x)=3x-4 "f at x is equal to 3x minus 4"
Quadratic parent function
y=x² or f(x)=x²
reciprocal parent function
y=|x| or f(x)=|x|
Square root parent function
y=√x or f(x)=√x
Set notation
{x∈R|0≤x≤50} "x belongs to the real number set such that x is greater than/equal to 0 and is less than or equal to 50